Measurement Error in Binary Explanatory Variables in Panel Data Models: Why Do Cross Section and Panel Estimates of the Union Wage Effect Differ?

Cross section estimates of the union wage effect are typically much larger than estimates derived from within estimators using panel data. Two competing explanations for this difference have been advanced. The first is that the cross section estimates suffer from an omitted variables bias due to a correlation between unobserved productivity and union status which biases the cross section estimator upwards. The second is that measurement error in union status is more severe in the changes than in the levels, imparting a more severe downward bias to the panel estimator. This paper derives a method of moments estimator which allows for both effects, nested within the same model. The binary nature of the explanatory variable is exploited to derive an estimating model which allows simultaneous estimation of both the structural parameters of the model and the parameters of the measurement error process. When the estimator is applied to sample of men from the PSID we find that allowing for measurement error does lead to a larger estimate of the union wage effect than the usual within estimator, but that most of the difference between the cross section and the panel estimates is not due to measurement error in the union variable. Further, the estimates of the extent of measurement error are close to those found in a validation study of the PSID.